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  • A Study of Proxies for Shapley Allocations of Transport Costs

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    Author(s)
    Aziz, Haris
    Cahan, Casey
    Gretton, Charles
    Kilby, Philip
    Mattei, Nicholas
    Walsh, Toby
    Griffith University Author(s)
    Gretton, Charles
    Year published
    2016
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    Abstract
    We survey existing rules of thumb, propose novel methods, and comprehensively evaluate a number of solutions to the problem of calculating the cost to serve each location in a single-vehicle transport setting. Cost to serve analysis has applications both strategically and operationally in transportation settings. The problem is formally modeled as the traveling salesperson game (TSG), a cooperative transferable utility game in which agents correspond to locations in a traveling salesperson problem (TSP). The total cost to serve all locations in the TSP is the length of an optimal tour. An allocation divides the total cost ...
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    We survey existing rules of thumb, propose novel methods, and comprehensively evaluate a number of solutions to the problem of calculating the cost to serve each location in a single-vehicle transport setting. Cost to serve analysis has applications both strategically and operationally in transportation settings. The problem is formally modeled as the traveling salesperson game (TSG), a cooperative transferable utility game in which agents correspond to locations in a traveling salesperson problem (TSP). The total cost to serve all locations in the TSP is the length of an optimal tour. An allocation divides the total cost among individual locations, thus providing the cost to serve each of them. As one of the most important normative division schemes in cooperative games, the Shapley value gives a principled and fair allocation for a broad variety of games including the TSG. We consider a number of direct and sampling-based procedures for calculating the Shapley value, and prove that approximating the Shapley value of the TSG within a constant factor is NP-hard. Treating the Shapley value as an ideal baseline allocation, we survey six proxies for it that are each relatively easy to compute. Some of these proxies are rules of thumb and some are procedures international delivery companies use(d) as cost allocation methods. We perform an experimental evaluation using synthetic Euclidean games as well as games derived from real-world tours calculated for scenarios involving fast-moving goods; where deliveries are made on a road network every day. We explore several computationally tractable allocation techniques that are good proxies for the Shapley value in problem instances of a size and complexity that is commercially relevant.
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    Journal Title
    Journal of Artificial Intelligence Research
    Volume
    56
    DOI
    https://doi.org/10.1613/jair.5021
    Copyright Statement
    © 2016 A I Access Foundation, Inc. The attached file is reproduced here in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.
    Subject
    Artificial intelligence
    Applied mathematics
    Cognitive and computational psychology
    Publication URI
    http://hdl.handle.net/10072/123928
    Collection
    • Journal articles

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